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Fluid Mechanics in Porous Media

02MAZNW

A.A. 2020/21

Course Language

Inglese

Course degree

Master of science-level of the Bologna process in Petroleum And Mining Engineering (Ingegneria Del Petrolio E Mineraria) - Torino

Course structure
Teaching Hours
Lezioni 80
Esercitazioni in aula 20
Tutoraggio 20
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Viberti Dario Professore Associato ING-IND/30 80 10 0 0 15
Teaching assistant
Espandi

Context
SSD CFU Activities Area context
ING-IND/30 10 B - Caratterizzanti Ingegneria per l'ambiente e il territorio
2020/21
The aim of the course consists in giving the fundamental concepts necessary to characterize, to understand and to describe analytically and numerically the behavior of fluids in porous media and, in particular the dynamic behavior of hydrocarbon reservoirs. The course is divided in some main chapters such as: reservoir fluids PVT properties; rock properties; rock fluid interaction properties; diffusivity equations for slightly compressible and compressible fluids. The course has to be considered as introductory to most of the other course of the petroleum engineering program.
The aim of the course consists in giving the fundamental concepts necessary to characterize, to understand and to describe analytically and numerically the behavior of fluids in porous media and, in particular the dynamic behavior of hydrocarbon reservoirs. The course is divided in some main chapters such as: reservoir fluids PVT properties; rock properties; rock fluid interaction properties; diffusivity equations for slightly compressible and compressible fluids. The course has to be considered as introductory to most of the other course of the petroleum engineering program.
Understanding the parameters used to characterize the dynamic behavior of fluid and of reservoirs, in terms of physical meaning and order of magnitude. Ability of approaching different technical problems by the selection the most suitable model. Critical approach in review to real data. Communication skills, ability of using and understanding the technical language and terminology adopted worldwide in the industries. Ability in increasing their own knowledge by selecting the appropriate technical and scientific literature.
Understanding the parameters used to characterize the dynamic behavior of fluid and of reservoirs, in terms of physical meaning and order of magnitude. Ability of approaching different technical problems by the selection the most suitable model. Critical approach in review to real data. Communication skills, ability of using and understanding the technical language and terminology adopted worldwide in the industries. Ability in increasing their own knowledge by selecting the appropriate technical and scientific literature.
Student should have an average background in physics, mathematics and Geology.
Student should have an average background in physics, mathematics and Geology.
Basics definitions and nomenclature Thermodynamic behavior of hydrocarbon mixtures: qualitative phase behaviour (PVT) of single and multi-component systems; hydrocarbon reservoir nomenclature and classification. quantitative phase behaviour of hydrocarbons: PVT parameters of gas, oil, and water. Fluid viscosity. Drive mechanisms and recovery factors. Static pressure profiles: hydrostatic equilibrium of hydrocarbon reservoirs; pressure gradients fluid contacts; interpretation of static pressure profiles for different reservoirs typology. Rock petrophysical properties: Routine core analyses; Porosity: total, effective, primary and secondary; Fluid saturation; Electrical conductivity: Archie's law. Basic concepts of log interpretation, mathematical models and numerical solutions. Darcy's law: hydraulic conductivity, permeability; generalized equation; Darcy's law in different flow geometries: linear, radial flow, vertical free flow, 3D flow. Permeability tensor, homogeneity and isotropy. Darcy's law for gases, slip flow and Klinkenberg effect. Forchheimer equation. Rock-fluids interaction properties: Special core analyses; Extension of Darcy's law to multiphase flow: effective permeability; relative permeability, mobility. Gas Oil Ratio. Superficial and interfacial tension, contact angle, wettability, immiscible fluids flow. Capillary pressure and capillary rise. J function; Imbibition and drainage; residual saturations. Diffusivity equation for monophase flow of slightly compressible fluids (oil and water): definition of the mathematical model; basic assumptions; analytical solutions in transient, steady and pseudo steady conditions, skin effect and productivity index; water encroachment. Diffusivity equation for monophase flow of highly compressible fluids (gas): diffusivity equations for laminar flow; analytical solution for turbulent flow, integration of Forchheimer equation under steady state conditions. Extension to pseudo-steady state and transient conditions. Turbolence skin and non-Darcy coefficient. Multiphase flow models: diffusivity equation in pressure and saturation; numerical models: fundamentals on Finite Difference Methods; treatment of non linearities, transmissibility.
Basics definitions and nomenclature Thermodynamic behavior of hydrocarbon mixtures: qualitative phase behaviour (PVT) of single and multi-component systems; hydrocarbon reservoir nomenclature and classification. quantitative phase behaviour of hydrocarbons: PVT parameters of gas, oil, and water. Fluid viscosity. Drive mechanisms and recovery factors. Static pressure profiles: hydrostatic equilibrium of hydrocarbon reservoirs; pressure gradients fluid contacts; interpretation of static pressure profiles for different reservoirs typology. Rock petrophysical properties: Routine core analyses; Porosity: total, effective, primary and secondary; Fluid saturation; Electrical conductivity: Archie's law. Basic concepts of log interpretation, mathematical models and numerical solutions. Darcy's law: hydraulic conductivity, permeability; generalized equation; Darcy's law in different flow geometries: linear, radial flow, vertical free flow, 3D flow. Permeability tensor, homogeneity and isotropy. Darcy's law for gases, slip flow and Klinkenberg effect. Forchheimer equation. Rock-fluids interaction properties: Special core analyses; Extension of Darcy's law to multiphase flow: effective permeability; relative permeability, mobility. Gas Oil Ratio. Superficial and interfacial tension, contact angle, wettability, immiscible fluids flow. Capillary pressure and capillary rise. J function; Imbibition and drainage; residual saturations. Diffusivity equation for monophase flow of slightly compressible fluids (oil and water): definition of the mathematical model; basic assumptions; analytical solutions in transient, steady and pseudo steady conditions, skin effect and productivity index; water encroachment. Diffusivity equation for monophase flow of highly compressible fluids (gas): diffusivity equations for laminar flow; analytical solution for turbulent flow, integration of Forchheimer equation under steady state conditions. Extension to pseudo-steady state and transient conditions. Turbolence skin and non-Darcy coefficient. Multiphase flow models: diffusivity equation in pressure and saturation; numerical models: fundamentals on Finite Difference Methods; treatment of non linearities, transmissibility.
The course is divided in 55-60% of theoretical background and 40-45% of exercises in the computer laib. During the exercises the students have to approach practical problems by applying the theory discussed during the lessons.
The course is divided in 55-60% of theoretical background and 40-45% of exercises in the computer laib. During the exercises the students have to approach practical problems by applying the theory discussed during the lessons.
Slides of the course available on line at the course web page for both theory and exercises. Additional material: E.J. Burcik. 1957. Properties of petroleum reservoirs fluids. John Wiley & sons, inc. London C.H. Whitson. M. R. Brule. 2000. Phase behavior. SPE Monograph Series. Richardson, Texas. C.R. Fitts. 2002. Groundwater science. Academic Press. London, UK A.T. Corey. 1977. Mechanics of heterogenous fluids in porous media. Water Resources Pubblications. Fort Collins, Colorado, USA D.W. Green, G.P. Willhite. 1998. Enhanced Oil Recovery. SPE Textbook Series vol.6
Slides of the course available on line at the course web page for both theory and exercises. Additional material: E.J. Burcik. 1957. Properties of petroleum reservoirs fluids. John Wiley & sons, inc. London C.H. Whitson. M. R. Brule. 2000. Phase behavior. SPE Monograph Series. Richardson, Texas. C.R. Fitts. 2002. Groundwater science. Academic Press. London, UK A.T. Corey. 1977. Mechanics of heterogenous fluids in porous media. Water Resources Pubblications. Fort Collins, Colorado, USA D.W. Green, G.P. Willhite. 1998. Enhanced Oil Recovery. SPE Textbook Series vol.6
Modalità di esame: Prova orale obbligatoria;
Exam: Compulsory oral exam;
The exam is aimed at evaluating knowledge, competences and skills acquired during the course. The exam will be oral through BBB platform. Oral questions are concerned with the theoretical parts and their application to synthetic problems. Furthermore, in order to access to the oral interview, each student has to prepare a report (word or pdf file) containing solutions of the assignments (exercises including numerical and/or symbolic calculations) given during the course. The report will be evaluated and the solution of the exercises could be part of the discussion during oral examination. Rules during online oral exams: students must show their identification document and this will be compared with the student’s photo available in the database of the University; a witness (who is not a member of the Board of Examiners) will be present during the exam; students must declare that they are not using any aid or support tool and that nobody is in the room to help them during the exam. Student must be alone in the room, on a table clean from papers/pad /phone or whatever else than pocket calculator, white papers, and a pen. The student might be asked to share the screen during questions. If the connection is lost, the exam will have to be restarted from the beginning. It is decision of the professor to offer opportunities for redoing the exam in case of technical problems.
Modalità di esame: Prova orale obbligatoria;
Exam: Compulsory oral exam;
The exam is aimed at evaluating knowledge, competences and skills acquired during the course. The exam will be oral through BBB platform. Oral questions are concerned with the theoretical parts and their application to synthetic problems. Furthermore, in order to access to the oral interview, each student has to prepare a report (word or pdf file) containing solutions of the assignments (exercises including numerical and/or symbolic calculations) given during the course. The report will be evaluated and the solution of the exercises could be part of the discussion during oral examination. Rules during online oral exams: students must show their identification document and this will be compared with the student’s photo available in the database of the University; a witness (who is not a member of the Board of Examiners) will be present during the exam; students must declare that they are not using any aid or support tool and that nobody is in the room to help them during the exam. Student must be alone in the room, on a table clean from papers/pad /phone or whatever else than pocket calculator, white papers, and a pen. The student might be asked to share the screen during questions. If the connection is lost, the exam will have to be restarted from the beginning. It is decision of the professor to offer opportunities for redoing the exam in case of technical problems.
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